Oscillating universes as eigensolutions of cosmological Schr\"odinger equation

We propose a cosmological model which could explain, in a very natural way, the apparently periodic structures of the universe, as revealed in a series of recent observations. Our point of view is to reduce the cosmological Friedman--Einstein dynamical system to a sort of Schr\"odinger equation whose bound eigensolutions are oscillating functions. Taking into account the cosmological expansion, the large scale periodic structure could be easily recovered considering the amplitudes and the correlation lengths of the galaxy clusters.